Details

sample93.0ms

Algorithm

intervals

Results

58.0ms	389×	body	80	valid
18.0ms	166×	body	80	nan

simplify225.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

225.0ms

(/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k)))

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.1b

localize33.0ms

Local error

Found 2 expressions with local error:

2.1b	(/ (* (pow k m) a) (fma (+ k 10) k 1))
0.0b	(* (pow k m) a)

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-exp-log`
12×	`add-sqr-sqrt`
9×	`add-cbrt-cube`
7×	`-un-lft-identity` `associate-l*` `add-cube-cbrt`
6×	`prod-exp`
4×	`unpow-prod-down` `div-exp`
3×	`associate-/r` `times-frac` `associate-r*` `unswap-sqr`
2×	`expm1-log1p-u` `pow-to-exp` `pow1` `cbrt-undiv` `pow-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp` `sqr-pow`
1×	`clear-num` `frac-2neg` `-commutative` `div-inv` `associate-/l`

Counts

2 → 54

Calls

2 calls:

Slowest

14.0ms	(/ (* (pow k m) a) (fma (+ k 10) k 1))
9.0ms	(* (pow k m) a)

series250.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

134.0ms	(/ (* (pow k m) a) (fma (+ k 10) k 1))
116.0ms	(* (pow k m) a)

simplify4.4s

Counts

40 → 60

Calls

40 calls:

Slowest

404.0ms	(* (* (* (pow k m) (pow k m)) (pow k m)) (* (* a a) a))
386.0ms	(/ (pow k m) (sqrt (fma (+ k 10) k 1)))
329.0ms	(/ (* (* (* (pow k m) a) (* (pow k m) a)) (* (pow k m) a)) (* (* (fma (+ k 10) k 1) (fma (+ k 10) k 1)) (fma (+ k 10) k 1)))
289.0ms	(- (log (* (pow k m) a)) (log (fma (+ k 10) k 1)))
283.0ms	(- (+ a (* (log k) (* m a))) (* 10 (* a k)))

prune819.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize34.0ms

Local error

Found 2 expressions with local error:

4.7b	(/ a (fma (+ k 10) k 1))
0.0b	(* (pow k m) (/ a (fma (+ k 10) k 1)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
21×	`times-frac`
19×	`*-un-lft-identity` `add-cube-cbrt`
17×	`add-exp-log`
13×	`associate-r`
9×	`add-cbrt-cube`
7×	`associate-l`
6×	`prod-exp` `unswap-sqr`
5×	`unpow-prod-down`
4×	`div-exp`
3×	`associate-/r` `associate-/l` `sqr-pow`
2×	`expm1-log1p-u` `pow-to-exp` `pow1` `cbrt-undiv` `pow-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp`
1×	`clear-num` `frac-2neg` `associate-r/` `-commutative`

Counts

2 → 76

Calls

2 calls:

Slowest

30.0ms	(* (pow k m) (/ a (fma (+ k 10) k 1)))
9.0ms	(/ a (fma (+ k 10) k 1))

series209.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

130.0ms	(* (pow k m) (/ a (fma (+ k 10) k 1)))
78.0ms	(/ a (fma (+ k 10) k 1))

simplify8.3s

Counts

71 → 82

Calls

71 calls:

Slowest

402.0ms	(- (+ (* 99 (* a (pow k 2))) a) (* 10 (* a k)))
323.0ms	(* (sqrt (pow k m)) (sqrt (/ a (fma (+ k 10) k 1))))
321.0ms	(+ (log (pow k m)) (- (log a) (log (fma (+ k 10) k 1))))
313.0ms	(* (pow k (/ m 2)) (/ (sqrt a) (sqrt (fma (+ k 10) k 1))))
297.0ms	(* (sqrt (pow k m)) (sqrt (/ a (fma (+ k 10) k 1))))

prune1.0s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize62.0ms

Local error

Found 4 expressions with local error:

4.7b	(/ a (fma (+ k 10) k 1))
0.5b	(cbrt k)
0.5b	(cbrt k)
0.5b	(cbrt k)

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`cbrt-prod` `times-frac`
6×	`add-cbrt-cube` `add-exp-log`
4×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `pow1/3` `associate-/l`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv`

Counts

4 → 72

Calls

4 calls:

Slowest

8.0ms	(/ a (fma (+ k 10) k 1))
1.0ms	(cbrt k)
1.0ms	(cbrt k)
1.0ms	(cbrt k)

series949.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

340.0ms	(cbrt k)
281.0ms	(cbrt k)
246.0ms	(cbrt k)
81.0ms	(/ a (fma (+ k 10) k 1))

simplify3.0s

Counts

46 → 84

Calls

46 calls:

Slowest

595.0ms	(- (+ (/ a (pow k 2)) (* 99 (/ a (pow k 4)))) (* 10 (/ a (pow k 3))))
348.0ms	(- (+ (* 99 (* a (pow k 2))) a) (* 10 (* a k)))
258.0ms	(- (+ (/ a (pow k 2)) (* 99 (/ a (pow k 4)))) (* 10 (/ a (pow k 3))))
196.0ms	(/ (* (* a a) a) (* (* (fma (+ k 10) k 1) (fma (+ k 10) k 1)) (fma (+ k 10) k 1)))
158.0ms	(* (pow (* k -1) 1/3) (cbrt -1))

prune1.2s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize39.0ms

Local error

Found 4 expressions with local error:

4.5b	(* a (/ 1 (fma (+ k 10) k 1)))
0.6b	(/ 1 (fma (+ k 10) k 1))
0.5b	(cbrt k)
0.5b	(cbrt k)

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
22×	`add-cube-cbrt`
20×	`times-frac`
17×	`add-exp-log`
13×	`associate-r`
11×	`add-cbrt-cube`
7×	`pow1`
6×	`cbrt-prod`
4×	`expm1-log1p-u` `div-exp` `prod-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `associate-l` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `rec-exp` `pow1/3` `1-exp` `cbrt-unprod` `div-inv`
1×	`clear-num` `frac-2neg` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `pow-flip` `inv-pow`

Counts

4 → 101

Calls

4 calls:

Slowest

18.0ms	(* a (/ 1 (fma (+ k 10) k 1)))
8.0ms	(/ 1 (fma (+ k 10) k 1))
1.0ms	(cbrt k)
1.0ms	(cbrt k)

series671.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

303.0ms	(cbrt k)
256.0ms	(cbrt k)
86.0ms	(* a (/ 1 (fma (+ k 10) k 1)))
27.0ms	(/ 1 (fma (+ k 10) k 1))

simplify5.7s

Counts

75 → 113

Calls

75 calls:

Slowest

556.0ms	(* (* (* a a) a) (/ (* (* 1 1) 1) (* (* (fma (+ k 10) k 1) (fma (+ k 10) k 1)) (fma (+ k 10) k 1))))
443.0ms	(* (* (* a a) a) (* (* (/ 1 (fma (+ k 10) k 1)) (/ 1 (fma (+ k 10) k 1))) (/ 1 (fma (+ k 10) k 1))))
436.0ms	(- (+ (* 99 (* a (pow k 2))) a) (* 10 (* a k)))
254.0ms	(- (+ (/ 1 (pow k 2)) (* 99 (/ 1 (pow k 4)))) (* 10 (/ 1 (pow k 3))))
247.0ms	(- (+ (/ a (pow k 2)) (* 99 (/ a (pow k 4)))) (* 10 (/ a (pow k 3))))

prune1.5s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

regimes193.0ms

Accuracy

98% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 1.9b

bsearch100.0ms

end0.0ms

sample3.2s

Algorithm

intervals

Results

2.2s	11931×	body	80	valid
618.0ms	4262×	body	80	nan